Guest column

Abstract

The complexity of counting problems has been studied intensively over the years. During the past decade, significant progress has taken place and a series of successively more powerful complexity dichotomies have been discovered. Given a class of counting problems, a dichotomy states that every problem in the class is either in polynomial time or #P-hard. In this guest column, we briefly survey two threads of recent developments in counting graph homomorphisms and the counting constraint satisfaction problem.